To determine The vertical reactions at A , B , and C . Explanation Given information: Consider A-36 steel shaft of diameter ( d ) of 1 in . The shaft is supported by the bearing at A and C . The bearing at B rests at the simply supported A-992 steel wide flange beam. The moment of inertia ( I ) of the shaft is 500 in . 4 The belt loads on the pulley is 400 lb . The moment of inertia of the beam ( I b ) is 500 in . 4 Calculation: Consider the Young’s modulus of the beam and the shaft are denoted by E b and E s , such that E b = E s = E Consider the moment of inertia of the beam and shaft are denoted by I b and I s . Show the deflection of the shaft as shown in Figure 1. Refer to Figure 1. Consider the deflections on beam are denoted by Δ b , ( Δ b ) 1 and ( Δ b ) 2 . The reaction at support B is denoted by B y . The load at the pulley is P = 800 lb . Show the expression for deflection ( Δ b ) 1 of shaft as follows: ( Δ b ) 1 = − P a b 6 E I s ( L ) ( L 2 − a 2 − b 2 ) (1) Substitute 800 lb for P , 10 ft for L, 3 ft for a , and 5 ft for b in Equation (1). ( Δ b ) 1 = − 800 ( 3 ) ( 5 ) 6 E I s ( 10 ) ( 10 2 − 3 2 − 5 2 ) = − 200 E I s ( 100 − 9 − 25 ) = − 200 E I s ( 100 − 9 − 25 ) = − 13 , 200 E I s The negative sign indicates that the deflection is in the downward direction. Show the expression for deflection ( Δ b ) 2 of shaft as follows: ( Δ b ) 2 = P L 3 48 E I s (2) Substitute B y for P and 10 ft for L. ( Δ b ) 2 = B y ( 10 ) 3 48 E I s = + 20.833 B y E I s The positive sign indicates that the deflection is in the downward direction. Show the deflection of the beam as shown in the Figure 2. Refer Figure 2. The deflection in the beam is denoted by Δ b . Show the expression for deflection ( Δ b ) 2 of beam as follows: Δ b = − P L 3 48 E I b (3) Substitute B y for P and 10 ft for L in Equation (3). Δ b = − B y ( 10 ) 3 48 E I b = − 20.833 B y E I b The negative sign indicates that the deflection is in the upward direction. Show the compatibility Equation as follows: Δ b = ( Δ b ) 1 + ( Δ b ) 2 (4) Substitute − 20

9th Edition

ISBN: 9789810694364

Author: Russell C Hibbeler

Publisher: Pearson Education

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Chapter 12.9, Problem 12.131P

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The vertical reactions at A, B, and C.

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Chapter 12.9, Problem 12.130P

Chapter 12.9, Problem 12.132P

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